# How do you evaluate 4.24\times 4.24?

Jan 15, 2017

$4.24 \times 4.24 = 17.9776$

#### Explanation:

Doing the calculation by hand, you could break it down as follows:

Starting with $4.24$, divide by $4$ to get $1.06 = 1 + 0.06$

Then:

$4.24 \times 4.24 = 4 \times \left(1 + 0.06\right) \times 4 \times \left(1 + 0.06\right)$

$\textcolor{w h i t e}{4.24 \times 4.24} = 16 \times {\left(1 + 0.06\right)}^{2}$

$\textcolor{w h i t e}{4.24 \times 4.24} = 16 \times \left(1 + 2 \left(0.06\right) + {0.06}^{2}\right)$

$\textcolor{w h i t e}{4.24 \times 4.24} = 16 \times \left(1 + 0.12 + 0.0036\right)$

$\textcolor{w h i t e}{4.24 \times 4.24} = 16 \times 1.1236$

$\textcolor{w h i t e}{4.24 \times 4.24} = 8 \times 2.2472$

$\textcolor{w h i t e}{4.24 \times 4.24} = 4 \times 4.4944$

$\textcolor{w h i t e}{4.24 \times 4.24} = 2 \times 8.9888$

$\textcolor{w h i t e}{4.24 \times 4.24} = 17.9776$

That may seem a little long-winded, but being able to double and halve numbers can often make arithmetic easier to do in your head.